Modular Arithmetic

Date: 11/08/2001 at 09:39:07
From: Chaim Lodish
Subject: Modular arithmetic
This is something my class has been working on, but we seem stuck.
For any integer a, a^4 is congruent to 0 or 1 (mod 5).
We get to the point where we let a = 2k and a = 2k+1 for both even
and odd cases, but are unable to get further to say that 16k^4 is
congruent to 0 or 1 mod 5.
We were able to work with the odd number case, and found at least ten
k's to be a factor of five. So it is just the even case that is
getting us stuck.
Many thanks,
Chaim